According to a report released in 2013, the airport with the highest on-time arrival rate has a 83.5% on-time rate. Choose 5 arrivals at random and find the probability that at least 1 was not on time.

59.41% probability that at least 1 was not on time.

Step-by-step explanation:

For each arrival, there are only two possible outcomes. Either it is on time, or it is not. The probability of an arrival being on time is independent from other arrivals, so we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

Find the probability that at least 1 was not on time.

Either all of them were on time, or at least one of them was late. The sum of the probabilities of these events is decimal 1. So

We want to find . So

In which

59.41% probability that at least 1 was not on time.

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.